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arXiv · 1612.02942

Riemannian Invariants that Characterize Rotational Symmetries of the Standard Sphere

Masayuki Aino
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Abstract

Inspired by the Lichnerowicz-Obata theorem for the first eigenvalue of the Laplacian, we define a new family of invariants $\{\Omega_k(g)\}$ for closed Riemannian manifolds. The value of $\Omega_k(g)$ delicately reflects the spherical part of the manifold. Indeed, $\Omega_1(g)$ and $\Omega_2(g)$ characterize the standard sphere.

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Masayuki Aino. 2016-12-09. Riemannian Invariants that Characterize Rotational Symmetries of the Standard Sphere. https://doi.org/10.1007/s00229-017-0969-9

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